1. Field of the Invention
The invention relates generally to the field of code division multiple access (CDMA). More particularly, the invention relates to CDMA pilot tracking for synchronization.
2. Discussion of the Related Art
Cellular telephony based on CDMA operates in two frequency bands in the US. The first band is the regular cellular band wherein base stations transmit using RF carrier frequencies of approximately 870 MHz. The second band is the PCS band wherein base stations transmit using RF carrier frequencies of approximately 1960 MHz. The principles of CDMA are well known and detailed specifications are established.(1-3) 
Fundamental to the operation of CDMA is the notion of the pilot channel which is transmitted by the base station. The sole purpose of the pilot channel is to allow the mobile station to acquire synchronization which is a prerequisite for extraction of any data (such as encoded speech). All CDMA base stations derive their timing from GPS (global positioning system) signals. Thus, any timing derived from the base station transmitted signal, namely the pilot channel is traceable to the GPS, provided the base station is not in a holdover mode of operation.
The pilot channel is a “constant” signal which, because of its deterministic nature, is suitable for acquisition and tracking. The “information” carried by the pilot channel is solely that of timing. It is generated by modulating a constant pattern onto the RF carrier. The construction of the pilot channel is depicted in FIG. 1.
The pilot channel is obtained by taking a constant pattern (e.g., all−1s) and spreading it using the I-channel and Q-channel PN (Pseudo Noise) sequences which have a chip-rate of 1.2288 Mcps. For convenience, the chip values are chosen as +1 and −1 though in an actual digital implementation the values would correspond to a logic-1 and logic-0, respectively. Following the spreading operation, the I and Q impulses are processed by identical baseband filters which provide the bandwidth limitation (intentional inter-symbol-interference) and pulse shaping functions. The I and Q channels are modulated onto the in-phase and quadrature RF carriers and summed to create the pilot channel signal s(t). The pilot channel and other channels (speech, paging, synchronization., etc.) are combined as a weighted sum so as the create the composite transmit signal whose power is nominally a constant. Thus, depending on the traffic, the radiated signal power associated with the pilot signal can be variable. Normal practice is to ensure that the pilot signal power is at least 10% of the radiated power.
The properties associated with the pilot channel are reflected directly in the ability of a receiver to extract proper synchronization. The fundamental aspects of the pilot channel are discussed below.
The I-channel and Q-channel PN sequences are periodic “noise-like” sequences which have a period of 215 chips. They are derived from PRBS (pseudo-random binary sequence; also referred to as maximum length linear feedback shift register sequences) which can be generated using 15-bit shift registers with appropriate feedback. A PRBS sequence has a period of (215−1) bits (i.e. chips) and is characterized by having strings of 1s of all lengths upto 15 but strings of 0s up to length 14. A PN sequence is created from the underlying PRBS sequence by inserting an additional 0 after the string of 14 zeros, which occurs only once per period in the PRBS. The period of the PN sequence is thus one more than the PRBS, or 215 bits (chips).
In IS-95 CDMA, the maximum length shift register sequences from which the PN sequences are derived are specified by the recursion relations:
i(n)=i(n−15)⊕i(n−10)⊕i(n−8)⊕(i(n−7)⊕i(n−6)⊕i(n−2)
q(n)=q(n−15)⊕q(n−12)⊕q(n−11)⊕q(n−10)⊕q(n−9)⊕q(n−5)⊕q(n−4)⊕q(n−3)
where i(n) and q(n) are binary-valued (‘0’ and ‘1’) and the additions are modulo-2. The ‘0’ inserted after the 14-th zero of the string of 14 consecutive zeros in the PRBS is, by definition, the “last” bit of the period; the subsequent ‘1’ is considered the first bit of the next period. The start of this first bit (chip) interval is aligned with CDMA system time.
The correlation between two sequences, {α(n)} and {β(n)}, where {α(n)} is assumed to be periodic with length N (bit-times), is defined as
      R          α      ⁢                          ⁢      β        =            ∑              n        =        0                    N        -        1              ⁢                  ⁢                  α        ⁡                  (          n          )                    ·              β        ⁡                  (          n          )                    This can be extended to the notion of an auto-correlation sequence and a cross-correlation sequence if it is assumed that the periods of the two sequences are the same. These extensions take the form
                                          R            αα                    ⁡                      (            k            )                          =                              ∑                          n              =              0                                      N              -              1                                ⁢                                          ⁢                                    α              ⁡                              (                n                )                                      ·                          α              ⁡                              (                                  n                  -                  k                                )                                                                                                  R            αβ                    ⁡                      (            k            )                          =                              ∑                          n              =              0                                      N              -              1                                ⁢                                          ⁢                                    α              ⁡                              (                n                )                                      ·                          β              ⁡                              (                                  n                  -                  k                                )                                                        where the correlation lag, k, indicates the delay introduced for the second sequence prior to computing the correlation.
PRBS sequences, generated using linear feedback shift registers, have an especially nice auto-correlation property. In particular, if {α(n)} is a PRBS sequence of length N=2K−1, and the values are treated as +1 and −1 (for ‘1’ and ‘0’), then the sequence Rαα(K) will be two-valued (and of course periodic) with Rαα(K)=N for k=0 and Rαα(K)=−1 for other values of correlation lag. That is, the auto-correlation sequence is (approximately) a Kronecker Delta function. This is the basis for considering such sequences “white-noise” or “white-noise-like.” Furthermore, the cross-correlation between two different PRBS sequences of the same length is approximately zero. Extending the PRBS sequences to the PN sequences by inserting an extra ‘0’ (or −1, depending on one's convention) does not alter the auto-correlation and cross-correlation properties to any great degree. Hence, the particular choice in IS-95 CDMA for generating the I-channel and Q-channel PN sequences.
For reference, the auto-correlation and cross-correlation properties of the I-channel and Q-channel sequences for IS-95 CDMA are listed directly below:
PRBS sequences:                Auto-correlation at zero-lag=32767        Maximum auto-correlation (magnitude) non-zero-lag=1        Maximum (magnitude) cross-correlation=257 (between I and Q) PN sequences:        Auto-correlation at zero lag=32768        Maximum auto-correlation (mag.) non-zero-lag=420 (I-channel)        Maximum auto-correlation (mag.) non-zero-lag=288 (Q-channel)        Maximum (magnitude) cross-correlation=676 (between I and Q)What is implied by these numbers is that the extension of the sequences from PRBS to PN in the manner chosen “degrades” the noise-like behavior of the sequences. Defining a figure of merit for a sequence as the ratio of auto-correlation at zero lag to the (magnitude) of the (largest) auto-correlation at non-zero lags, it can be appreciated that there is a minor degradation. A second figure of merit relates to the distinguishability between the two sequences and can be defined as the ratio of the auto-correlation at zero lag to the (largest magnitude) cross-correlation (for any lag). There is a degradation of about 8 dB inherent in the extension of the PRBS to PN sequences.        
The auto-correlation properties of the PN sequences allows for the determination of the presence as well as the position of the pilot in the received radio frequency (RF) signal. Where the RF signal has been translated to baseband and sampled at the chip-rate, and denoting by {α(n)} the (periodic) normalized I-channel PN sequence (with values +1 and −1), the received signal can be modeled asr(n)=A α(n−K)+η(n)where {η(n)} represents the signal component other than the I-channel pilot and is modeled, for simplicity, as a white noise sequence of power σ2. The signal-to-noise ratio is, therefore, given by
  SNR  =                    A        2                    σ        2              ⁢                  ⁢    or    ⁢                  ⁢          20      ·                        log          10                ⁡                  (                      A            σ                    )                      ⁢    dB  The operation of correlating this received signal with (delayed) versions of the known I-channel sequence (or “template”) will now be considered. The computed correlation sequence will be designated as {R(k)} and is given by
      R    ⁡          (      k      )        =                    ∑                  n          =          0                          N          -          1                    ⁢                          ⁢                        r          ⁡                      (            n            )                          ·                  α          ⁡                      (                          n              -              K                        )                                =                  N        ·        A        ·                  δ          ⁡                      (                          k              -              K                        )                              +                        ∑                      n            =            0                                N            -            1                          ⁢                                  ⁢                              η            ⁡                          (              n              )                                ·                      α            ⁡                          (                              n                -                k                            )                                          assuming the auto-correlation of the I-channel sequence takes the form of a Kronecker Delta function. Thus, the correlation will “peak” at a lag of K chips. But, this peak may be obscured somewhat by the contribution of the correlation between the template and the noise component of the received signal (everything other than the I-channel pilot sequence component). If the “noise” component is white and uncorrelated with the I-channel sequence, then the obfuscation of the true peak has a mean value of zero and a variance equal to Nσ2. The “signal” power, namely the power associated with the correlation peak, is N2A2 and thus the “despreading” of the code provides an SNR improvement of 10 log10(N) dB, or about 45 dB.
IS-95 CDMA specifies a pulse-shaping filter; the baseband filter depicted in FIG. 1. The pulse shaping filter functions as a spectrum conditioning filter and is nominally a lowpass filter whose passband extends to 590 kHz and stopband starts at 740 kHz (the transition band is 590 kHz to 740 kHz). The passband ripple must be less than 1.5 dB and minimum stopband attenuation must be 40 dB. The manner in which it is specified indicates that Qualcomm Inc. (who originated IS-95) implements this filter as an FIR filter operating at a sampling rate of 4*1.2288 MHz (4 times chip rate). In fact the FIR filter is described as a length 48 FIR filter with even symmetry and the coefficients, {h(n); n=0,1, . . . , 47}, provided in IS-95.
The generation of the filtered I-channel and Q-channel signals is depicted in FIG. 2 explicitly shows just the I-channel. The Q-channel is similar.
The chip-rate PN sequence, {i(n)}, is oversampled by inserting 3 zeros between successive samples to yield the signal {α(n)} at the higher sampling rate of 4.9152 MHz (4 times the chip-rate). The output of the 48-point FIR filter provides {γ(n)}, the spectrum-shaped I-channel pilot signal (still at base-band). The period is now 4*215=217 samples (4 samples per chip). The auto-correlation of the signal {α(n)} is much the same as the correlation of the PN sequence itself and can be approximated by the Kronecker Delta function. The cross-correlation between {α(n)} and {γ(n)} is not, however, a Delta function but takes on the shape of the impulse response of the FIR filter. Specifically,
            R              α        ⁢                                  ⁢        γ              ⁡          (      k      )        =                    ∑                  n          =          0                          N          -          1                    ⁢                          ⁢                        α          ⁡                      (            n            )                          ·                  γ          ⁡                      (                          n              -              k                        )                                =                            ∑                      m            =            0                    47                ⁢                                  ⁢                              ∑                          N              =              0                                      N              -              1                                ⁢                                          ⁢                                                    α                ⁡                                  (                  n                  )                                            ·                              α                ⁡                                  (                                      n                    -                    k                    -                    m                                    )                                                      ⁢                          h              ⁡                              (                m                )                                                        =              h        ⁡                  (          k          )                    using the approximation that the auto-correlation of {α(n)} is indeed a Delta function. Thus, the correlation sequence follows the impulse response of the filter. The filter, having symmetric coefficients, introduces a flat delay of 23.5 samples, effectively moving the peak of the correlation sequence. It also introduces a spread; the correlation sequence is not a Delta function anymore. The filter coefficients, normalized to a maximum of unity, have the following behavior around the mid-point:h(19)=h(28)=−0.1405; h(20)=h(27)=0.0946; h(21)=h(26)=0.4414 h(22)=h(25)=0.7858; h(23)=h(24)=1.0The implication of this spread is that if the correlation is done at the chip-rate without a “matched” filter, then there will be an uncertainty as to the true “peak” since two correlation values will be nominally equal and the presence of any noise may cause a shift one way or the other, introducing a systemic uncertainty of (¼)-chip in the estimate of the peak.
The matched filter is used prior to computing the correlation. Since the baseband filter is symmetric, the matched filter is the same and thus the correlation spread is governed by the impulse response of the filter obtained by convolving {h(n)} with itself. It can be shown that the operation of matched filtering improves the situation by providing a unique peak. For the filter specified in IS-95, the result of convolving the filter with itself gives rise to impulse response coefficients which are described below for 10 lags around the peak (the filter is symmetric):
h*h(0)=3.94; h*h(1)=3.54; h*h(2)=2.48; h*h(3)=1.14 h*h(4)=−0.029
h*h(5)=−0.697; h*h(6)=−0.772; h*h(7)=−0.408; h*h(8)=0.101 h*h(9)=0.465
If these values are normalized to a maximum (central peak=unity), the following results are obtained:
h*h(0)=1.0; h*h(1)=0.898; h*h(2)=0.629; h*h(3)=0.289 h*h(4)=−0.007
h*h(5)=−0.177; h*h(6)=−0.196; h*h(7)=−0.104; h*h(8)=0.026 h*h(9)=0.118
It is seen that the peak value (un-normalized) and the correlation value offset by one sample (which is a quarter-chip) are 3.94 and 3.54, respectively. Consequently, the presence of noise may cause an error in picking the correct peak but if the post-correlation SNR is greater than 20 dB, the probability of this occurring is less than about 0.33 (33% of the time). Secondary peaks are also present but the highest secondary peak (greater than 4 lags from the true peak) is down about 14 dB.
However, implementing this matched filter, even assuming undersampling by a factor of 4 to reduce the sampling rate to the chip-rate, requires roughly 60 million multiplies per second for each of the I- and Q-channels. This is well beyond the capabilities of any current off-the-shelf DSP, especially if the DSP has to do any other task at all! When integrated into an ASIC as a specialized function it is feasible and may be performed in the Qualcomm chip-set.
The pilot tracking method is depicted in the simplified block diagram shown in FIG. 3. The RF signal is translated down to baseband (center frequency=0 Hz, i.e., dc). FIG. 3 shows a single translation whereas in practice a dual down-conversion scheme will be employed with an IF frequency where a (usually SAW) filter is used to define the channel selected. The term (t-τ) relating to the LO signal indicates that the LO phase and the transmitter carrier phase may be different. The in-phase and quadrature demodulated signals are passed through a matched filter, denoted by H*(f), and sampled at the chip-rate (1.2288 MHz) though the phase of the sampling clock may be adjustable. This is indicated by showing the sampling “starting” at time=t0 with samples taken every Tc units of time (Tc is the chip-interval). The sampled in-phase and quadrature signals are correlated using the I-channel and Q-channel PN sequences as templates in a “complex” fashion which is necessitated since the relative phase of the LO and transmit oscillators is an unknown (but assumed fixed) value. The value t0 is varied over the range required (one period of the PN sequences, i.e., 215 chips). During the “acquisition” phase, to speed up the time for acquisition, the correlation may be done over a partial period.
The Qualcomm Reference design, which is used by all CDMA mobile handsets uses a 19.68 MHz VCXO which is “locked” to the code-rate by the pilot tracking method which uses a conventional “early”, “late”, and “on-time” correlation mechanism. The RF signal is translated to in-phase and quadrature signals centered at dc and lowpass filtered prior to A/D conversion (one converter for the in-phase and one for the quadrature). The conversion clock is derived from the 19.68 MHz VCXO and it has been observed that this derived sampling clock is not smooth but does have some jitter. The “matched filter” is implemented using DSP. A general block diagram depicting the Qualcomm reference design is shown in FIG. 4.
The sampling jitter and the imperfection of matching between the two A/D converters and the mismatch between the two lowpass filters (pre-A/D-conversion filters) cause errors in the tracking of the pilot. Therefore, what is needed is an approach that tracks the pilot signal with greater accuracy.
The IS-95 specification calls for the base-station signal processing chain to include an allpass filter, ostensibly to compensate for the non-linear-phase characteristics of the pre-A/D filter called for in the Qualcomm reference design. Any design not using the Qualcomm reference design and integrated circuits (for which a significant license fee is charged) must circumvent the impact of this allpass filter which Qualcomm has mandated for the base-station in the IS-95 specification. Therefore, what is also needed is an approach that avoids the Qualcomm reference design and integrated circuits and simultaneously circumvents the impact of the allpass filter.